Computed Ganymede-Callisto two-working-body ballistic cycler gc-1 (k = 3, both moons bend)

ganymede-callisto-two-working-body-cycler-gc1-2026 · source: this-project · validation: V2 · candidate

Signature

Bodies: Ganymede-Callisto
Primary: Jupiter
Sequence (canonical): Ganymede-Callisto-Callisto-Ganymede
Sense: n/a
Orbit class: Cycler
strict cycler (infinite returns)
Cycler class: multi-arc
Trajectory regime: ballistic
Maintenance ΔV band: unclassified
Model assumption: circular-coplanar
Idealised: planets on circles, coplanar ecliptic.
Period: — yr (3 × Ganymede-Callisto synodic)
DERIVED (this project): 3 Ganymede-Callisto synodic periods = 37.570 d in the Russell & Strange 2009 Table 2 ideal model. Encounters per period: Ganymede 2, Callisto 2.
Source ephemeris: ideal circular-coplanar Galilean model (Russell & Strange 2009 Table 2 constants); real-ephemeris patched-conic rung on NAIF jup365; continuous-gravity ideal-model rung
Ephemeris model the source states its numbers were computed against.
Priority date: 2026-10-06

V∞ at encounters

Ganymede (encounter 1): 2.40 km/s
DERIVED (this project, ideal-model patched-conic zero; data/943_cell_gc_gauntlet.json). Ganymede turn 2 x 29.35 deg, ratio 0.646 of the 100-km-floor capacity, required altitude 2,437 km. Continuous gravity (full mass): 2.130 km/s.
Callisto (encounter 2): 1.81 km/s
DERIVED (this project). Callisto turn 2 x 40.15 deg, ratio 0.737 of the 200-km-floor capacity, required altitude 1,801 km. Continuous gravity (full mass): 1.785 / 1.843 km/s.

Cycle-level identity (multi-arc invariants)

Aphelion ratio (AR): —
Turn ratio (TR): —
Transit times (days): 10.578 d, 6.512 d, 16.689 d, 3.79 d

Multi-arc (no single ellipse). Distance from Jupiter 888,745-2,294,675 km (all legs, the Callisto full-rev included; data/942_943_extent_rereport.json).

Orbit view 2.5D ecliptic projection

spacecraft: idealized coplanar ellipse planets: J2000 osculating ellipse (Standish & Williams Table 1) orientation: coplanar-idealized (no Ω/ω published — in-plane ellipse)

3D view not available for multi-arc trajectories yet. The 3D system can now render a numerically-sampled polyline (n-body or multi-arc), but no sampled trajectory is published for this row — each leg is a separate ellipse with honest gaps where elements are unpublished (the 2D view above shows them). The button will appear here once a sampled path is exported for this trajectory; we never interpolate one from the catalogue's per-leg (a, e).

— — planet orbit (true J2000 ellipse)

Definition status

incomplete — core fields missing or known-unknowns tracked below

Known-unknowns (1)

Values we expect to exist but have not yet filled (distinct from "not applicable"). Tracked per upstream docs/spec.md §16.6.4.

vinf_kms_at_encounters [unknown]
Real-ephemeris continuous-gravity standing untested: the open-chain n-body formulation does not converge across a full-revolution return; the ideal-model continuous-gravity closure stands; the real-ephemeris pass is the patched-conic chain tool (rung (d)); obstruction: out-of-plane mismatch across the full-revolution leg.

source: docs/notes/2026-10-08-1034-gc1-continuous-sigma.md sec. 9; (f83eac79)

Primary citation

No primary citation recorded; see the provenance tags below.

orbit fidelity circular-coplanar V∞ fidelity circular-coplanar

Corroborating sources

Hollister, W. M. & Menning, M. D. (1970). Periodic Swing-By Orbits between Earth and Venus. Journal of Spacecraft and Rockets 7(10):1193-1199. DOI: 10.2514/3.30134
METHOD source: the two-working-body date-residual corrector (matched |V_inf| at every flyby by iterating the encounter dates), generalised here to the Jovian moons.
Russell, R. P. & Strange, N. J. (2009). Cycler Trajectories in Planetary Moon Systems. Journal of Guidance, Control, and Dynamics 32(1):143-157. DOI: 10.2514/1.36610
MODEL source: the ideal circular-coplanar Galilean model and its return taxonomy. Their ideal-model cyclers have one working body and a massless target (AAS 07-118 p.2). AAS 07-118 p.18 names 'removing the massless assumption of the target body' as future work, 'the Jovian system cyclers in particular'.
Campagnola, S. et al. (2019). Tour Design Techniques for the Europa Clipper Mission. Journal of Guidance, Control, and Dynamics 42(12):2615-2626. DOI: 10.2514/1.G004309
PRIOR ART, nearest published two-working-body Ganymede-Callisto cycler: ONE published example (GCGC, sec. III.C, Fig. 11): strictly alternating G-C-G-C flybys, V_inf 3.5/4.5 km/s, high fidelity, no states. It is a single trajectory, not a searched class or family, so spec §16.4 known-class-member does not apply (owner ruling 2026-10-07). gc-1 has a different structure: G-G and C-C returns, V_inf 2.40/1.81 km/s.

Notes

First computed two-working-body ballistic Ganymede-Callisto cycler of this structure (both moons bend at every encounter), k = 3 (37.570 d). Legs: a Ganymede 1-rev low return (10.58 d), G->C (6.51 d), a Callisto 1:1 full-revolution return (16.69 d) and C->G (3.79 d). Ideal-model Lambert-leg starts 1.178102, 11.756379, 34.957696 d (model epoch: all bodies at angle 0 at t = 0). Results note: docs/notes/2026-10-05-942-943-two-working-body-generator.md secs. 6.11, 6.26, 6.45, 6.56. Owner summary: docs/notes/2026-10-06-942-943-owner-decision-summary.md sec. 2.1. Real-ephemeris standing (patched conic, NAIF jup365, 10 cycles = 376 d): - The chain closes ballistically and passes the gate at 5/5 epochs 2030-2056 (worst 0.755-0.761); DOP853 re-fly <= 0.19 km. - The Jovian full-rev path is validated by the published controls GanCal#1@2013 (R-S Fig. 9(b); closes, re-fly 2.8e-4 km, gate indeterminate as in their ideal model; owner ruling 6.45) and GanEur#316@2019 (half-rev path, gate pass). - screen (amendment 2.6, data/973_screen_943_gc.json): passes r_min > Jupiter radius plus floor, and no interior pass inside either moon's SOI. Continuous gravity (docs/notes/2026-10-08-1034-gc1-continuous-sigma.md sec. 9; ideal model with point-mass moons at real GMs, not the ephemeris): gc-1 EXISTS. - Its joint-mass branch runs from sigma = 0.05 to 1 with no fold. Identity by the limit at sigma = 0.005: V_inf G 2.3944, C 1.8068/1.8070, against the patched-conic 2.397/1.807. - Full-mass orbit: Ganymede V_inf 2.130 km/s, altitudes 2,962-2,964 km; Callisto V_inf 1.785 / 1.843 km/s, altitudes 1,965 / 2,842 km. IAS15 re-fly 2.4e-6 km. - The -0.27 km/s Ganymede shift against the patched conic is the same order as the controls; not a failure criterion (sec. 8.2). - Real-ephemeris continuous-gravity standing untested: the open-chain n-body formulation does not converge across a full-revolution return (gc-1's 16.7-d Callisto 1:1 leg, and the same for the GanCal#1 control). The real-ephemeris pass is the patched-conic chain tool (rung (d)). V2-ballistic (spec §14 owner amendment 2026-10-08, same-phase drift wording of 2026-10-11; docs/notes/2026-10-08-1007-v2-ballistic-chain-campaign.md secs. 8.4b, 8.11-8.12): PASS at 5 of 5 jup365 epochs, 10 continuous cycles each (L = 4; the chain's first and last cycle excluded from the comparisons). - Junction |V_inf| continuity 8.6e-7 km/s against the 1e-6 criterion (a narrow margin). - Same-phase drift: dates 0.013-0.037 d against a 0.185-d band; |V_inf| 0.005-0.008 km/s against 0.175. - Slope diagnostics (handed to V3): dates -0.0023 to +0.0001 d per cycle; |V_inf| -0.0008 to +0.0006 km/s per cycle. - Systematic real-versus-ideal |V_inf| offset (recorded, not banded): up to 0.079 km/s. History: first promoted at 3/5 (MARGINAL) under the sec. 7 rules, which were amended after seeing results (recorded as such); re-judged under the final owner wording. Controls: Hollister-Menning 1970 orbit 1 from its printed dates passes; a broken chain fails. Literature: - Scripted gate (literature_check v2,; data/942_943_litcheck_scope.json): INCONCLUSIVE. Named anchor: "Russell-Strange 2009 Ganymede-Callisto ideal-model moon cycler" (one working body). Rule F7: a different-architecture object at a system the source treated goes to a human. - Resolving notes: docs/notes/2026-10-06-943-gc-prior-art-search.md; results note 6.41, 6.44, 6.53. No collision in 21F31 ISSFD 2024, Golubev 2014/2017, Lam 2015/2018, Buffington 2012/2014, Lynam papers, Takubo et al. 2026, Boutonnet 2024 or Minovitch 1972. - Owner decision 2026-10-08: the gate's inconclusive is decided by the owner's 2026-10-07 ruling, candidate-novel. Attribution: Hollister & Menning 1970 (method), Russell & Strange 2007/2009 (model), Campagnola et al. 2019 (nearest prior art). - Further prior art (corpus review, docs/notes/2026-10-07-971-fable-corpus-review-2.md lines 54-76): - Minovitch 1972 (JSR 9(10):751, p.755) defines "periodic GT trajectories" among the Galilean satellites, judges four-moon ones "rather remote" and computes none (concept prior art). - Grushevskii, Golubev et al., ISSFD 2017, p.3: GAM chains with "closed cycles of Ganymede flybys... provided that Callisto is passed intermediately", a Tisserand-graph loop inside a one-way descent. No period, V_inf or altitude is printed. - Boutonnet et al. 2024 (JUICE, Space Sci. Rev. 220:67, pp.33-34, 38, 40): a one-shot C-G-C round trip, both moons bending, Callisto V_inf 5.22 -> 1.8-2.4 km/s, 7 or 8 Ganymede periods between Callisto passes over the 50-day cycle. It is the nearest published two-moon relative by V_inf, but not periodic. - Takubo et al. 2026 (AIAA SciTech 2026-1262, p.4): "subsets of free-return trajectories, such as the Ganymede-Callisto cycler, have been explored... no generalized families of such transfers are known". Its own solutions are one-way escape tours with minimum V_inf Ga 6.0, Ca 4.5 km/s (Table 3). - Wording: "first computed", never "new class".